There is an ever-increasing need in the automotive field for efficient and accurate models since the calibration of the motor control system is becoming increasingly complex, and also increasingly expensive due to stricter and stricter regulatory requirements. The principal requirements for good models are good measurement data and an appropriately selected measurement design. As a result, the number of measurements and thus also the measurement period increases. However, since time on the test stand is very expensive, the need arises for effective experimental designs that minimize the number of measurement points, cover the test space as effectively as possible, while at the same time not qualitatively degrading the models trained using these data. These models are then used to optimize and calibrate ECU structures, or also to make decisions regarding components.
Optimal experiment design (OED) optimizes the information content, which is demanded to properly parametrize a model with as little effort as possible, as explained in L. Pronzato “Optimal experimental design and some related control problems.” Automatica, 44(2):303-325, 2008. Dynamic excitation signals are characterized by their spacial distribution and their temporal behaviour. For the identification of linear dynamic systems pseudo random binary signals (PRBS) are commonly used, see G. C. Goodwin and R. L. Payne “Dynamic System Identification: Experiment Design and Data Analysis” Academic Press Inc., New York, 1977. When it comes to nonlinear dynamic systems amplitude modulated pseudo random binary signals (APRBS) are well established as excitation signals, in order to track the nonlinear process characteristics, see e.g. O. Nelles “Nonlinear System Identification: From Classical Approaches to Neural Networks and Fuzzy Models” Springer, Berlin, 2001. In contrast to these very general methodologies for the experiment design, model based design of experiments (DoE) is more specifically suited to the process to be identified in that a prior process model or at least a model structure is used to maximize the information gained from experiments.
Real processes are subject to restrictions, which basically affect system inputs and outputs. E.g. the manipulated and the control variables must not exceed the feasible range, in order to provide specified operational conditions or to prevent damage from the plant. For the consideration of system output constraints in the DoE a model is required, which predicts the output dynamics. Model based DoE can also be used for online experiment design, where the model is continuously adapted to incoming data and the DoE is generated sequentially for a certain number of future system inputs. Such a procedure is commonly called online or adaptive DoE and is depicted in FIG. 1. Explanations can be found in Online Dynamic Black Box Modelling and Adaptive Experiment Design in Combustion Engine Calibration, Munich, Germany, 2010 and in László Gerncsér, Hakan Hjalmarsson and Jonas Martensson “Identification of arx systems with nonstationary inputs—asymptotic analysis with application to adaptive input design” Automatica, 45:623-633, March 2009.